https://doi.org/10.48550/arXiv.2405.04033

Summary

  • Periodic and quasi-periodic can help reveal properties of underlying object.
  • Three methods for discovering periodicity: Lomb-Scargle periodogram (LSP), weighted wavelet Z-transform (WWZ), and Gaussian process regression
  • Compare their results on two X-ray light curves from Swift that accompanied short gamma-ray bursts (sGRB).
  • Found periodicity but needs to be confirmed
  • Detrending was the biggest factor affecting the recovery of periods.
  • Suggest X-rays originate from magnetar oscillations after binary merger or precession of newborn magnetar.

Data

  • 124 sGRBs in third Swift-BAT catalogue (12/2004–07/2019)
  • 67 BAT light curves with SNR > 3
  • Chose 2 light curves with sufficient data:
    • GRB 050724
    • GRB 060614
  • Used points from the initial WT (windowed timing) mode, not latter PC (photon counting) mode.

Data: sGRB 050724

Data: sGRB 060614

Methodology (Raw light curve)

  • Fit GP
    • Mean function: power law, polynomial.
    • kernel: quasiperiodic, simple harmonic oscillator, damped random walk.
  • Inspect hyperparameters
    • period, P
    • quality factor, Q > 0.5

Methodology (Detrending)

Detrend by subtracting from raw light curve

  • Fitted GP
    • Mean: power law, kernel: quasiperiodic.
    • Mean: power law, kernel: damped random walk.
    • Mean: polynomial, kernel: quasiperiodic.
    • Mean: polynomial, kernel: simple harmonic oscillator.
    • Mean: polynomial, kernel: damped random walk.
  • Fitted polynomial

Methodology (Detrended light curve)

  • Fit GP
    • Mean function: constant.
    • kernel: quasiperiodic, damped random walk.
  • Calculate L-S periodogram
  • Apply WWZ-transform

Results

Results

Results

Results

Conclusions

  • Potential QPOs were detected.
  • LSP, WWZ, and GPs seem consistent.
  • Detrending has large influence, as does kernel and mean function.

Comments

  • No recommendations on which method to use and why.
  • Spent too much time describing celerite, could just cite.
  • Conclusion contradicts results.

Statistical nitpicking

  • Detrending is like enforcing stationarity
  • Detrending itself is not trivial; what order polynomial was used?
    • equivalent to non-zero GP mean function
  • Heavy selection bias (n = 2)
  • Fitting Gaussian likelihood to X-ray data
  • Using MLE to initialise MCMC is good practice

Hmmm…